Gas Turbines for Aircraft Propulsion Gas turbines The

Gas Turbines for Aircraft Propulsion

Gas turbines The turbojet engine consists of three main sections: the diffuser, the gas generator, and the nozzle. The diffuser placed before the compressor decelerates the incoming air relative to the engine. A pressure rise known as the ram effect is associated with this deceleration.

Gas turbines The gas generator section consists of a compressor, combustor, and turbine, with the same functions as the corresponding components of a stationary gas turbine power plant. The gases leave the turbine at a pressure significantly greater than atmospheric and expand through the nozzle to a high velocity before being discharged to the surroundings.

Gas turbines The working fluid is air modeled as an ideal gas. The diffuser, compressor, turbine, and nozzle processes are isentropic, and the combustor operates at constant pressure. In an actual engine, there would be increases in specific entropy across the diffuser, compressor, turbine, and nozzle.

Gas turbines Process a– 1 shows the pressure rise that occurs in the diffuser as the air decelerates isentropically through this component. Process 1– 2 is an isentropic compression. Process 2– 3 is a constant-pressure heat addition. Process 3– 4 is an isentropic expansion through the turbine during which work is developed. Process 4– 5 is an isentropic expansion through the nozzle in which the air accelerates and the pressure decreases.

Gas turbines In a typical thermodynamic analysis of a turbojet on an air-standard basis, the following quantities might be known: the velocity at the diffuser inlet, the compressor pressure ratio, and the turbine inlet temperature (at 3). The objective of the analysis would be to determine the velocity at the nozzle exit. Once the nozzle exit velocity is determined, the thrust is determined by applying Newton's second law of motion in a form suitable for a control volume

Example 9. 12 Air enters a turbojet engine at 11. 8 lbf/in. 2, 430°R, and an inlet velocity of 620 miles/h (909. 3 ft/s). The pressure ratio across the compressor is 8. The turbine inlet temperature is 2150°R and the pressure at the nozzle exit is 11. 8 lbf/in. 2 The work developed by the turbine equals the compressor work input. The diffuser, compressor, turbine, and nozzle processes are isentropic, and there is no pressure drop for flow through the combustor. For operation at steady state, determine the velocity at the nozzle exit and the pressure at each principal state. Neglect kinetic energy at the exit of all components except the nozzle and neglect potential energy throughout.

Air enters a turbojet engine at 11. 8 lbf/in. 2, 430°R, and an inlet velocity of 620 miles/h (909. 3 ft/s). The pressure ratio across the compressor is 8. The turbine inlet temperature is 2150°R and the pressure at the nozzle exit is 11. 8 lbf/in. 2

Each component is analyzed as a control volume at steady state. The control volumes are shown on the sketch by dashed lines. The diffuser, compressor, turbine, and nozzle processes are isentropic. There is no pressure drop for flow through the combustor. The turbine work output equals the work required to drive the compressor.

Except at the inlet and exit of the engine, kinetic energy effects can be ignored. Potential energy effects are negligible throughout. The working fluid is air modeled as an ideal gas. Analysis: To determine the velocity at the exit to the nozzle, the mass and energy rate balances for a control volume enclosing this component reduce at steady state to give

Except at the inlet and exit of the engine, kinetic energy effects can be ignored. Potential energy effects are negligible throughout. The working fluid is air modeled as an ideal gas. Analysis: To determine the velocity at the exit to the nozzle, the mass and energy rate balances for a control volume enclosing the nozzle are applied.

Energy rate balances for a control volume enclosing the nozzle

The inlet kinetic energy is dropped by the assumption that kinetic energy effects can be ignored except at the inlet and exit of the engine.

Solving for V 5

With the operating parameters specified, the determination h 4 and h 5 values is accomplished by analyzing each component in turn, beginning with the diffuser. The pressure at each principal state can be evaluated as a part of the analyses required to find the enthalpies h 4 and h 5.

Table A-22 E ha (at 430 R) =102. 7 Btu/lb T=420 R, h = 100. 32 btu/lb T=440 R, h = 105. 11 btu/lb Energy rate balance for a control volume enclosing the diffuser gives

Table A-22 E h = 114. 69 btu/lb, pr = 0. 9182 h = 119. 48 btu/lb, pr = 1. 0590 Interpolation at h = 119. 2 btu/lb, pr 1 = 1. 051 Table A-22 E T=420 R, pr = 0. 5760 T=440 R, pr = 0. 6776 Interpolation pa (at 430 R) = 0. 6268 The flow through the diffuser is isentropic, so pressure p 1 is

p 1 = 19. 79 lbf/in. 2 Using the given compressor pressure ratio, the pressure at state 2 is p 2 = 8(19. 79 lbf/in. 2) = 158. 3 lbf/in. 2 The flow through the compressor is also isentropic. Thus Table A-22 E p = 7. 761, h = 211. 35 Btu/lb r pr = 8. 411, h = 216. 26 Btu/lb Interpolation h 2 (at pr = 8. 408) = 216. 2 Btu/lb

At state 3 the temperature is given as T 3 = 2150°R. Table A-22 E T= 2150°R, h = 546. 54 Btu/lb From Table A-22 E, h 3 = 546. 54 Btu/lb. By assumption of no pressure drop for flow through the combustor, p 3 = p 2. The work developed by the turbine is just sufficient to drive the compressor. That is

Solving for h 4

h 4 = 449. 5 Btu/lb Table A-22 E h = 436. 12 btu/lb, pr = 101. 98 h = 449. 71 btu/lb, pr = 114. 0 Interpolation at h 4 = 449. 5 btu/lb, pr 4 = 113. 8 The expansion through the turbine is isentropic, so With p 3 = p 2 = 158. 3 lbf/in. 2 and pr 3 data from Table A-22 E at h 3 = 546. 54 btu/lb, pr 3 = 233. 5

The expansion through the nozzle is isentropic to p 5 = 11. 8 lbf/in. 2 thus From Table A-22 E, h 5 = 265. 8 Btu/lb, which is the remaining specific enthalpy value required to determine the velocity at the nozzle exit.

Using the values for h 4 = 449. 5 Btu/lb and h 5 = 265. 8 Btu/lb determined above, the velocity at the nozzle exit is

Combined Gas Turbine–Vapor Power Cycle A combined power cycle couples two power cycles such that the energy discharged by heat transfer from one cycle is used partly or wholly as the input for the other cycle.

The stream exiting the turbine of a gas turbine is at a high temperature. This high-temperature gas stream can be used by the combined cycle shown, involving a gas turbine cycle and a vapor power cycle. The two power cycles are coupled so that the heat transfer to the vapor cycle is provided by the gas turbine cycle, which may be called the topping cycle.

The combined cycle has the gas turbine's high average temperature of heat addition and the vapor cycle's low average temperature of heat rejection, and thus a thermal efficiency greater than either cycle would have individually. For many applications combined cycles are economical, and they are increasingly being used worldwide for electric power generation.

The thermal efficiency of the combined cycle is the net power developed by the gas turbine is the net power developed by the vapor cycle is the total rate of heat transfer to the combined cycle, including additional heat transfer, if any, to superheat the vapor entering the vapor turbine.

For steady-state operation, negligible heat transfer with the surroundings, and no significant changes in kinetic and potential energy, energy balance around the heat exchanger gives Combined cycle performance can be analyzed using mass and energy balances. To complete the analysis, however, the second law is required to assess the impact of irreversibilities and the true magnitudes of losses.

Combined cycle performance can be analyzed using mass and energy balances. To complete the analysis, however, the second law is required to assess the impact of irreversibilities and the true magnitudes of losses. Among the irreversibilities, the most significant is the exergy destroyed by combustion. About 30% of the exergy entering the combustor with the fuel is destroyed by combustion irreversibility.

Definition of exergy: Exergy is the maximum theoretical work obtainable from an overall system consisting of a system and the environment as the system comes into equilibrium with the environment (passes to the dead state). The exergy of a system, E, at a specified state is given by the expression

The exergy of a system, E, at a specified state is given by the expression U, KE, PE, V, and S denote, respectively, internal energy, kinetic energy, potential energy, volume, and entropy of the system at the specified state. U 0, V 0, and S 0 denote internal energy, volume, and entropy, respectively, of the system when at the dead state. In this chapter kinetic and potential energy are evaluated relative to the environment. Thus, when the system is at the dead state, it is at rest relative the environment and the values of its kinetic and potential energies are zero. Death state: the system comes into equilibrium with the environment— that is, as the system passes to the dead state.

Neglecting changes in kinetic and potential energies, the net rate of exergy increase for an open system is given by mg = mass flow rate through the system To = surrounding temperature

Example 9. 13: A combined gas turbine–vapor power plant has a net power output of 45 MW. Air enters the compressor of the gas turbine at 100 k. Pa, 300 K, and is compressed to 1200 k. Pa. The isentropic efficiency of the compressor is 84%. The condition at the inlet to the turbine is 1200 k. Pa, 1400 K. Air expands through the turbine, which has an isentropic efficiency of 88%, to a pressure of 100 k. Pa. The air then passes through the interconnecting heat exchanger and is finally discharged at 400 K. Steam enters the turbine of the vapor power cycle at 8 MPa, 400°C, and expands to the condenser pressure of 8 k. Pa. Water enters the pump as saturated liquid at 8 k. Pa. The turbine and pump of the vapor cycle have isentropic efficiencies of 90 and 80%, respectively.

A combined gas turbine–vapor power plant has a net power output of 45 MW. Air enters the compressor of the gas turbine at 100 k. Pa, 300 K, and is compressed to 1200 k. Pa (at 2). The isentropic efficiency of the compressor is 84%. The condition at the inlet to the turbine is 1200 k. Pa, 1400 K. Air expands through the turbine, which has an isentropic efficiency of 88%, to a pressure of 100 k. Pa (at 4).

The air then passes through the interconnecting heat exchanger and is finally discharged at 400 K. Steam enters the turbine of the vapor power cycle at 8 MPa, 400°C, and expands to the condenser pressure of 8 k. Pa (at 8). Water enters the pump as saturated liquid at 8 k. Pa. The turbine and pump of the vapor cycle have isentropic efficiencies of 90 and 80%, respectively. Let T 0 = 300 K, p 0 = 100 k. Pa.

From the temperature of relative pressure, the enthalpy and entropy at 9 states can be determined and listed in the following table:

State 1: T 1 = 300 K h 1 = 300. 19 k. J/kg, pr 1 = 1. 3860 State 2: p 2 = 1200 k. Pa For adiabatic compression from p 1 to p 2: Therefore pr 2: = pr 1 = 1. 3860 From Table A-22 pr = 16. 28, h = 607. 02 k. J/kg pr = 17. 30, h = 617. 53 k. J/kg = 16. 6320

From Table A-22 pr = 16. 28, h = 607. 02 k. J/kg pr = 17. 30, h = 617. 53 k. J/kg h 2, isen = 607. 02 + (16. 632 16. 28)*(617. 53 607. 02)/(17. 30 16. 28) h 2, isen = 610. 647 k. J/kg h 2 = h 1 + (h 2, isen h 1)/0. 84 = 300. 19 + (610. 647 300. 19)/0. 84 h 2 = 669. 7817 k. J/kg

State 3: T 3 = 1400 K h 3 = 1515. 42 k. J/kg, pr 3 = 450. 5 State 4: p = 100 k. Pa Adiabatic expansion from 1, 200 k. Pa to 100 kpa From Table A-22 pr = 37. 35, h = 767. 29 k. J/kg pr = 39. 27, h = 778. 18 k. J/kg h 4, isen = 767. 29 + (37. 5417 37. 35)*(778. 18 767. 29)/(39. 27 37. 35) h 4, isen = 768. 3773 k. J/kg h 4 = h 3 + 0. 88*(h 4, isen h 3) = 1515. 42 + 0. 88*(768. 3773 1515. 42) h 4 = 858. 0224 k. J/kg

State 7: T 7 = 400 o. C, p 7 = 8 MPa From steam table or CATT 2 program (Computer Aided Thermodynamic Tables 2) h 7 = 3138. 3 k. J/kg, s 7 = 6. 3633 k. J/kg K Isentropic expansion to state 8, p 8 = 8 k. Pa h 8, isen = 1989. 9 k. J/kg h 8 = h 7 + 0. 90*(h 8, isen h 7) = 3138. 3 + 0. 90*(1989. 9 3138. 3) h 8 = 2104. 7 k. J/kg State 9: Saturated liquid at 8 k. Pa: h 9 = 173. 86 k. J/kg, s 9 = 0. 59254 k. J/kg K

State 9: Saturated liquid at 8 k. Pa: h 9 = 173. 86 k. J/kg, s 9 = 0. 59254 k. J/kg K Isentropic compression to state 6: 8 MPa h 6, isen = 181. 9 k. J/kg h 6 = h 9 + (h 6, isen h 9)/0. 8 = 173. 86 + (181. 9 173. 86)/0. 8 h 6 = 183. 91 k. J/kg

Apply energy balance to the heat exchanger: mg(h 4 h 5) = mv(h 7 h 6)

The net power developed by the gas turbine is given by

The net power developed by the steam turbine is given by